The spatial noise generates a spurious image which degrades the useful image or even renders it unusable: assuming that the scene observed by the sensor is an image of uniformly average luminance, the sensor supplies a non-uniform image, which is unacceptable if this non-uniformity exceeds a certain degree; furthermore, the observed image depends on the level of this uniform luminance, which renders this noise that much more of a nuisance when the behavior difference of two pixels depends on the luminance that they receive.
The behavior of the pixels differs in fact from one pixel to another not only with regard to the signal level produced for a reference luminance level, but also with regard to the growth gradient of the response curve of the pixel according to the luminance.
To minimize the spatial noise generated in this way in a matrix sensor, it has already been proposed to measure the output signal levels of the different pixels for a uniform image of given luminance and to individually shift the signal level of each pixel so that all the pixels are brought to one and the same reference (first order correction). It has also been proposed to record the levels for two different uniform luminance levels, in order to correct not only the level shift but also the variation gradient (second order correction).
To correct both the level and the gradient, after having measured the signals obtained from each pixel for two different uniform luminances, it is possible, for example, to proceed as follows:                in the first step, a correction is made which brings the level of the signal to one and the same value that is common to all the pixels for one of the uniform illumination levels, a value that can be considered to be a reference value;        in the second step, after having shifted the signal level of each pixel by a value specific to this pixel, a gain correction is carried out so that the variation gradient around the reference value of the corrected signal is the same for all the pixels; for each pixel, the difference between the corrected signals obtained for the two luminances is calculated, and, for each pixel, a gain is determined such that this difference multiplied by the gain is equal to a value common to all the pixels; a correction is then made for each pixel which consists in multiplying the difference between the corrected signal level and the reference value by the gain specific to this pixel; this gives a doubly-corrected signal that is added to the common reference value to obtain the final signal.        
These methods therefore require in practice, to take into account the level dispersion and to take into account the gain dispersion, a manual calibration based on one or two uniform images presenting reference luminances, which is problematic; moreover, this calibration must be redone if the spatial noise drifts over time.
It has also been proposed to make corrective calculations for each of the dots of the collected image, based on the observation of a large number of successive images, by assuming that the statistical average and the statistical variance of the light levels received by a pixel is the same for all the pixels because of the diversity of the images received over time. Thus, the average is calculated of the signals received over time for each pixel and the current signal from the pixel is corrected to shift the current level by a value corresponding to the difference between the average detected for this pixel and a reference average value common to all the pixels. This brings the average level of all the signals to one and the same reference value, this reference value being derived from a statistical average and not from the observation of a screen of reference uniform luminance.
Similarly, the variance is calculated for each pixel over a large number of images, this variance in a way representing an approximation of the gradient of the variation curve of the signal level according to the luminance, and a gain correction is applied to the current signal variations, the correction being the difference between the calculated variance and a reference variance common to all the pixels. The reference variance can be an average of the variances of all the pixels. This brings the variation gradient of each pixel to one and the same reference value.
This solution is highly advantageous since it requires no calibration from reference screens.
However these calculations are very intensive since they require a large number of images to be collected, all of them to be stored, average calculations to be made for each pixel over this large number of images, and variance calculations on each pixel. In practice, this can be done only by a powerful computer, on prestored series of images. It would not be possible to collect and directly process the image in the shot-taking camera. Consequently, although this solution can be used in theory to process pre-recorded images, it is not at all applicable for taking instantaneous images.
In a certain number of image sensors, the dispersion of the signal levels for a given average luminance proves to be much greater than the dispersion due to the gradient variance over the entire possible luminance scale. Typically, if the amplitude of the signal variations within the range of useful luminances gives rise to a signal dispersion from pixel to pixel of the order of an eighth of this amplitude, the dispersion of the average amplitude of the signal, from pixel to pixel, can be as high as eight times the amplitude of the variations in the useful range. This also results from the fact that the signal variations obtained from the pixel, within the range of luminances that can be received, often do not exceed 1 to 2 percent of the average level of the electrical signal supplied by the pixel. It is therefore particularly crucial in these sensors to correct the dispersion of the response levels.
However, it has been seen that, for a certain number of image sensors that have a very high level dispersion, the dispersion of the variation gradients from one pixel to another is correlated with the dispersion of the average signal levels for a given luminance: in practice, the variation gradient of the output signal according to the luminance is greater if the level for an average luminance is higher. This results from the physical construction of these image sensors. Such is the case in particular for bolometric-type infrared sensors.